Abstract:

The premium functional on capacity space was investigated, and the results prove that the premium functional that satisfies monotonicity of the distribution, comonotonic additivity and normativity can be represented as Choquet integral with respect to the distorted capacity. And then the theorem of the existence and uniqueness of the distorted function g and some related properties of the distorted capacity were obtained.

Key words:  premium functional; Choquet integral; capacity; capacity space